Question

Line through the points (−2, 6) and (4, 8) is perpendicular to the line through the points (8, 12) and (x, 24). Find the value of x.

Answer 1

Let the given points be A (−2, 6), B (4, 8), P (8, 12) and Q (x, 24).

Slope of AB = m₁ = $\frac{8-6}{4+2}=\frac{2}{6}=\frac{1}{3}$

Slope of PQ = m₂ = $\frac{24-12}{x-8}=\frac{12}{x-8}$

It is given that the line joining A (−2, 6) and B (4, 8) and the line joining P (8, 12) and Q (x, 24) are perpendicular.

$$\begin{gathered} \therefore m_1{m}_2=-1 \\ \Rightarrow \frac{1}{3}\times \frac{12}{x-8}=-1 \\ \Rightarrow x-8=-4 \\ \Rightarrow x=4 \end{gathered}$$

Hence, the value of x is 4.